Abstract

The Cyclic Redundancy Check (CRC) is a technique for detecting errors in digital data, but not for making corrections when errors are detected. It is used primarily in data transmission. In the CRC method, a certain number of check bits, often called a checksum, are appended to the message being transmitted.

The receiver can determine whether or not the check bits agree with the data, to ascertain with a certain degree of probability whether or not an error occurred in transmission.

If an error occurred, the receiver sends a “negative acknowledgement” (NAK) back to the sender, requesting that the message be retransmitted. Basically the CRC is based on polynomial arithmetic, in particular, on computing the remainder of dividing one polynomial in GF (2) (Galois field with two elements) by another.

It is a little like treating the message as a very large binary number, and computing the remainder on dividing it by a fairly large prime such as intuitively, one would expect this to give a reliable checksum.

The technique is also sometimes applied to data storage devices, such as a disk drive. In this situation each block on the disk would have check bits, and the hardware might automatically initiate a reread of the block when an error is detected, or it might report the error to software. The material that follows speaks in terms of a “sender” and a “receiver” of a “message,” but it should be understood that it applies to storage writing and reading as well